Let f(x) and g(x) be irreducible polynomials over a field

Chapter 18, Problem 5SE

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Let f(x) and g(x) be irreducible polynomials over a field F. If f(x) and g(x) are not associates, prove that \(F[x] /\langle f(x) g(x)\rangle\) is isomorphic to \(F[x] /\langle f(x)\rangle \oplus F[x] /\langle g(x)\rangle\).

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